The value of 'a' when $a x^{3} + 9 x^{2} + 4 x - 10$ is divided by $x + 3$ leaving a remainder of 5 is ___

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Solution

Given - when $a x^{3} + 9 x^{2} + 4 x - 10$ is divided by $x + 3$ the remainder is 5.

$\Rightarrow$ $a (- 3)^{3} + 9 (- 3)^{2} + 4 (- 3) - 10 = 5$

$\Rightarrow$ $- 27 a + 81 - 12 - 10 = 5$

$\Rightarrow$ $a = 2$

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